2. That which is agreed upon by others to be true at any moment. It is shared, consensual, social, ephemeral, objective. Fads and fashions are real enough in this sense, but they are a kind of collective hypnosis. This corresponds to second person in grammar. In this sense Elvis Presley was a great singer.

3. That which is absolutely and eternally true, without regard to opinions, culture, context or time. Examples are ideals, archetypes, and mathematical facts, such as the relationships between p, i and e, Euclid and Pythagoras.

Laws of aesthetics, ethics and logic are in this category of thirdness. Leibnitz’s law of identity is in this category, as are the famous laws of form of D’Arcy Thompson and G. Spencer Brown. Thirdnesses are frequently called Platonic because of Plato’s exhaustive treatment of form.

Intuition is “the power to distinguish at a glance the essence amid the Accidents.” – Schopenhauer.

Thinking, according to the Oxford English Dictionary (OED) and the American Heritage Dictionary is “forming in the mind.” Thinking includes symbol manipulation, and deduction. Mentation is a broader term that includes thinking as well as experiencing, feeling, acting, instincting, and intuiting. Reasoning is one of many kinds of thinking.

Consciousness is the continuum of states of sentience, and expression. It includes quales, dreams, knowing, reasoning and influencing. Most mentation is beneath the threshold of awareness, but it is all in the domain of consciousness. Interesting examples are driving your car, waking up at night when the clock stops, a musician flowing in her music, idiot savants, and many optical illusions. The term sub-aware is meaningful but the term sub-conscious is a null set. We are always conscious as any anesthesiologist is well aware.

Logos. “A Greek word, of great breadth of meaning, signifying the intelligible principle structure, or order which pervades something, or the source of that order, or giving an account of that order. The cognate verb legein means ‘say’, ‘tell’, ‘account.’ Hence the ‘word’ which is ‘in beginning’ as recounted at the start of St John’s gospel is. logos. The root occurs in many English compounds such as biology, epistemology, geology, psychology, … The idea of a generative intelligence (logos spermatikos) is a profound metaphysical notion in Neoplatonic discussion. – Oxford Encyclopedia of Philosophy Cosmic reason, affirmed in Greek philosophy as “the source of world order and intelligibility, the self-revealed in the thought and will of God,” from the American Heritage Dictionary and the OED.

The domain of logic includes, but is not limited to, semiotic, linguistics, mathematics, grammar and rhetoric. Knowledge is derived from the Sanskrit jnana, to know plus the Latin ledge, to bind

METAPHOR

Metaphor, in Greek, means “to carry across.” In Athens a shopping cart in the supermarket is called a metaphor.

Semiotic is a more precise and general term for what we usually call metaphor. Semiotic bridges diction to notion, the essence. The existence of semiotic proves the existence of essence. Some of the technical types of semiotic are – allegory, allusion, ambiguity, anagogy, analogy, eponym, four senses of interpretation (hermeneutics), hebraic parallelism, hyperbole, icon, index, irony, map, metaphor, metonym, polysemous meaning, pun, sarcasm, sardony, sign, simile, synecdochy, symbol, token, trope.

Every word is a metaphor, a conveyor, for an idea or an experience.

God (good) is a new word in the Bible, not occurring before about 1000 AD. The word is only a very inadequate metaphor pointing to the essence of all essences. In the Christian Trinity, the concept of GOD breaks down into

1) the community of Spirit, the “Holy Ghost,” the ancient Hindu concept of Idandra,

2) the organizing and motivating principle of the Universe, “the Father,” in Sanskrit, Brahman, and

3) your essence, the Messiah, the “Son,” in Sanskrit atman. The etymological meaning of the word “GOD” does not do justice to what is implied by the concept.

Art is metaphor, pointing to essence. Think of the message of Hildegaard of Bingen, the romantic poets, the luminist painters, the impressionists, Schubert and Beethoven. As in poetry, their message to you is embedded between the words. Maria Montessori tells of feeding her hungry dog – “Don’t look at my finger pointing, look at the bone!”

All experience is ineffable. Therefore all communication is approximate, at best. Therefore the best education is one that cultivates the use and understanding of metaphor.

Education is teaching poetry, as Robert Frost told the faculty at Amherst in 1931. Everything is metaphor. Essence exists, but it is not a thing. Experience is 100% essence. Here is a neat little paradox –

4) therefore the nomothetic is always wrong, the idiographic is always right.

All communication is intrinsically embedded in this process. A similar paradox holds for general (always wrong) versus particular (always right). Blake said – “all men are alike in outward form (and with the same infinite variety).” Our faces are all alike, yet never alike!

DIRECT KNOWING

Definition of knowing – to perceive essence. Knowing is experiential, firstness, self-evident. Knowing is always direct. Great art is known by its experiential authority. Abraham “knew” Sara. He perceived her essence.

SCIENTIFIC METHOD

1. Guess (hypothesize) a model (a pattern in the data) in the domain you want to understand.

2. Get data. Measure all you can. Optimize your precision.

3. Share the data and models with others. Attain reproducibility. Science is necessarily social, consensual. The philosopher C.S. Peirce calls the community of science a synechism where the shared belief is definitive, yet ever changing, evolving.

4. Triangulate the data from every possible aspect.

5. Guess a better model (metaphor), using formal criteria for the qualities of better models. [See the section, “WAYS TO EVALUATE ONTOLOGIES” at the end of the book.]

6) Go to 2).

MEASUREMENT

The trouble with measurements is that they are always in error. There is no way to avoid them. To begin with, accuracy is always with regard to some standard. Standards (models, ideals) are always abstractions, never actually observed. Models are always in flux, as new data comes in and more refined theories are contrived. Models evolve by trial and error, and good taste. Thereby accuracy drifts, and is never fully attained. Precision. Any number of data points may seem to be orderly, but cusps, major discontinuities and craziness can occur between any two ‘normal’ points.

Quantum Indeterminacy (Heisenberg) is intrinsic. The act of measuring perturbs the object that is being measured, as any kindergarten teacher knows.

Entropy. Any measuring engine suffers from friction, as stated by the Second Law of Thermodynamics.

Consider: A grapefruit cannot be cut exactly in half, for these four independent reasons: Accuracy. What is the standard for comparison? 1/2 by weight? 1/2 by volume? 1/2 by surface area? 1/2 by juice content? … Whatever standard you choose, it cannot be exactly known just where the halfway plane (manifold) is, because any grapefruit and any physical sphere is irregular. And any standard from which to reference ‘accurate’ is arbitrary. Precision. involves the measuring engine. The knife cannot be passed through the desired center plane because of the intrinsic error of positioning and controlling the knife.

Indeterminacy. The interface between the two halves is fuzzy and fundamentally unknowable in exact detail!

Entropy. Any cutting engine suffers from friction that will deflect the cut. Error, as derived from these four sources, drives evolution. Sin (error) is the process by which God expresses the universe.

PROOF

What constitutes proof? The materialist would ‘prove’ the theorem of Pythagoras by making as many experiments (measurements) on fuzzy right triangles, ‘as many as he needs.’ But this, at best, would only demonstrate or suggest the theorem. Proof can not exist in the domain of science because of the aforementioned limitations. But we can prove abstractions such as the fact that an infinite sequence approaches a limit, such as e, and p. *) Proof may be gained through deduction. For example, the binary search theorem, Brouwer’s theorem, Pythagoras’ theorem, the laws of aesthetics, Euclid’s theorems, and de Morgan’s laws. Consider, most of these are not in the domain of mathematics. Mathematics is only a proper subset of the larger domain of the absolute, Logos. *)

Proof can never be gained through measurements, nor through induction, interpolation, extrapolation, abstraction, nor inference. Because of the many contributors to indeterminacy in measurement, proof and certainty can never be attained in the material domain. Proof does not apply in the domain of experience. But patterns in experience are shareable, e.g., birth, death, art. Logos is beyond experience, but is eminently shareable.

Proof (certainty) always goes beyond experience, and that is the value of it.

Proof permits us to extrapolate experience. Wittgenstein’s penultimate book is titled Certainty. Jerome Bruner’s masterpiece is entitled On Knowing, Essays for the Left Hand. Day to day examples of sharable ideals are maps. Directions given in terms of east and west are superior to those given in terms of right and left, which are relative to the observer’s position, which is unknown if the observer needs directions! I am a dualist in the sense that proof exists (abounds) in the absolute, never in Nature – the contrast between physics and psychics. I am a monist in the sense that the absolute and the manifest are not-two. As elaborated by e.a. Cummings, Hermes Trismegistus, Advaita Vedanta and Hui Neng, the Sixth Patriarch of Buddhism in China.

LEIBNITZ’S LAW

Leibnitz’s Law states that two individuals are identical if and only if they are alike in every attribute. Here is an example of a law of the Absolute – not dealing in any way with manifest things, or numbers, not relating to other facts or data. Here is a law of logic, a fact without an object! My friend came to visit us. Quoting William James, I said, “Saying ‘no’ is better than saying ‘yes’ ” (niti-niti). Joining in the spirit of the game, he said, “proving ‘same’ is completely different and much more difficult than proving ‘different’.” Now this is a very elemental basic fundamental part of thinking, discriminating, distinguishing between “same” and “different.” In Sanskrit the word is “Vijnana,” categorizing. It is easy to establish that two entities are different – simply compare corresponding attributes of each entity until we encounter the first one that does not match. Done.

Admittedly, just to identify an attribute is a subjective categorization, an intuitive “clad” decision. And all categorizations are tentative. But to prove same-ness is beyond the reach of rigor. To establish that two entities are the same requires that all attributes are compared, an indeterminate and infinite regress! Here even matching correspondences in the sense of Cantor fails, because, unlike numbers, a delineation of qualities cannot even be defined. To conclude that two entities are the same is a flight of fancy, a leap of faith, an abstraction. Comparing DNA in blood samples can establish innocence (different), but cannot establish guilt (same). No one can even demonstrate (pattern match) that a pine tree in the forest is actually a pine tree, considering the infinite number of potential variations between an actual, phenomenal pine and the textbook ideal. Since there are no two alike, which one is the ‘real’ pine tree? But one can abstract it. And that abstraction is like no pine tree found in Nature, past, present, or future.

Science has to proceed on that tenuous basis. In this regard, as well as in many others, science operates in blind faith, as a religion, guessing (believing) from hierarchies of known, suspected, unknown, and unknowable subjectivities. Digest this, it is centrally important. The laws of falsifiabilty, so important in science, law and reason, as emphasized by Peirce, Bridgman, Ayer and Popper derive from Leibnitz.

LOGOS

Logos takes its central place along with aesthetics, ethics, and metaphysics. The universe is characterized by form and color (qualia). Logos is the domain of the laws of form. Logos deals with eternals, including, but not restricted to archetypes. Qualia deal with ephemerals, the phenomenal. Most of the domain of logos lies beyond the field of proof, but some of the principles, amazingly, can be proven. For example, the optimality of the binary search can be proven. Cantor’s relationships of the transfinite numbers can be proven. Many mysterious relationships involving p, e and i can be proven.

One of the most powerful tools in the logos, in the unmanifest universe, is the principle of niti-niti, (not-this, not-this), as expounded by the ancient Indians. This principle is the basis of all science (vijnana) and lies at the core of the scientific method.

Sciences, (as well as many other domains, such as law, rationality, thinking, telephone books, and data bases), begin with and have their foundations in taxonomy, distinctions. The foundation of thinking, and of languages of all sorts, is categorization – something is in this category because it is not in the others! Someone else will come along and make entirely different categories, with just as much justification. Niti-niti, for example, is the process by which you distinguish a rose from other plants in a garden. Say you have a list of plants in the city park. With a botanical key, you can demonstrate that the rose is not a tree, not a clover, not a raspberry, and so on. What remains as the only possibility on the list is a rose, all the other plants on the list having been excluded. You have proven that the plant is a rose by a process of successive negation. Every positive identification is a result of eliminating all other possibilities, niti-niti.

Michaelangelo sculpted his masterworks by chiseling away all of the granite that did not belong there. Bach said, “playing the organ is easy, just don’t let your fingers play any of the wrong notes.” Kabbalah says that God wrote the Laws of the tablets by taking away the irrelevant parts of the stone. William James said, saying “no” is better than saying “yes.” Meditators advocate the “via negativa.” Two individuals in nature can easily be proven to be different, if in fact they are. But they can never be proven to be the same, even if they are, because that would require an infinite number of comparisons of pairs of attributes. DNA testing can prove innocence, but it can never prove guilt. To prove innocence, just compare characteristics of the blood samples, pair by pair, until you find a pair of that does not match. Done.

Rigorous. Suspect innocent. But to prove guilt, to prove that the samples are the same, requires an infinite regress – all characteristics up to the present point in the comparison match, but they always have an infinite way yet to go, more attributes yet to find (conceptualize), an unbounded number of matches to establish before the first mis-match. You can prove that a rose is not a walnut, but you can never prove that a rose is a rose! We know that a rose is a rose only by an inferential leap! How many attributes does a rose have? Answer – an infinite number. That is why the problem of “sameness” becomes a non-converging infinite regress. It is impossible to prove that an entity X is a pine. Each pine has an infinite number of qualities, so they cannot be exhaustively compared, pair by pair. To assert that X is a pine is an abduction. The description in the pine manual is an idealization – another abduction. There can never be a pine in nature that is the same as the one in the manual. There can not even exist two pines in nature that are the same, let alone identical with the one in the manual! This is the place where the problem of clads comes in.

A cladistic tree is a diagram showing relationships (in biological evolution or in any other developmental situation). The problem is, the characteristics we choose to distinguish one taxon from another are arbitrary and subjective. Anyone else may draw a perfectly reasonable tree based on a completely different set of distinguishing features. And so ad infinitum. Well, this whole line of thinking is rigorous and productive and commonplace. But it is not mathematics, nor is it linguistics. It is a reality that does not operate in the domain of time or space, materiality, history, culture, opinion, consensus, aesthetics or perception. It is logos, the mysterious core of all other reality.

Other exquisite examples of logos, form without objects, are the laws of the transfinite numbers formulated by Georg Cantor, and the domain of complex variable. DeMorgan’s Law, states that the truth of a logical paragraph is preserved when all elements are negated and all unions and intersections are inverted. It is the backbone of the fortunes of Silicon Valley. The syntax of a grammatical statement can be proven to be either rigorously correct or in error.

REDUCED vs. EMERGENT

How do snowflakes turn into avalanches? How do neuron firings turn into moods? Reduction means breaking things down into component parts. Everything is a reduction. Reduction can be carried on without limit.

Atoms are built of nucleons, which are built of quarks, which are built of subquarks, and so on. On the other hand, and equally true – everything is an epiphenomenon.

Laws at one level of organization aren’t related to laws at higher and lower levels. For example, the laws of meteorology that govern tornadoes cannot, in practice, be arrived at by studying the motion of the component molecules of gas. The psychology of mobs at soccer matches cannot be derived from the laws of individual psychology. Laws of behavior cannot be derived from an understanding of the action in the synapses. Very different laws operate at different levels of organization, and even between different levels of organization.

Beyond reduction lies complexity and chaos. Without exception, everything at every level is complex and chaotic. And so ad infinitum. Reduction is a “will-o-the-wisp”!

SOKOL’S HOAX

Sokol, a young Princeton physicist, published, tongue-in-cheek, an article seeming to be in support of postmodernist views. A few weeks later he published in a similar journal that the whole thing was a spoof, using silly postmodern jargon. The postmoderns were deeply offended and complained. Steven Weinberg, a distinguished Nobel physicist, came to Sokol’s defense in the New York Review of Books, August 1996, p11.

Sokol made a sarcastic “appeal to fashionable academics who question the claims of science to objectivity.” “Postmoderns in the humanities … who see the laws of nature as social constructions.” He attacks the ideologies of “postmodern intellectuals, social constructivists, relativists, new critics, and other trendy leftists in the humanities” following the oracle of deconstruction, Jacques Derrida.” They interpret modern catastrophe theory / chaos theory to support their ideas that all reality is a social construct depending upon consensual foundations. Quite to the contrary,

“Nature is strictly governed by impersonal mathematical laws. There exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole.” And there are many external worlds, other than Nature, such as the world of logos and the world of epistemology. “Most postmodernists deny that they have any doubt about the existence of an external world,” they believe in an objective reality …

On relativism – “If objective reality exists, then what scientists say is either true or false. If true, then how can it depend on the social environment of the scientist?” (e.g. sexist, racist, classicist, culturally coercive.) “Physics and chemistry, mathematics and logic, bear the fingerprints of their distinctive cultural creators no less than do anthropology and history.” “We did not create the Laws of physics.” “.. if we ever discover intelligent creatures on some distant planet and translate their scientific works, we will find that we and they have discovered the same laws.”

“The objective nature of scientific knowledge is taken for granted by most natural scientists.” (secondness) On entrenched authority – “the direction of physics (science) today is overwhelmingly set by young physicists, who are not yet weighed down with honors or authority, and whose influence – the excitement they stir up – derives from the objective progress that they are able to make.

“Science is cumulative, and permits definite judgments of success or failure.” It is evolving in the accumulative, Lamarckian sense. Lamarckian evolution operates much faster than Darwinian evolution, which is genetic. Salamanders that fall into caves without light lose their functional eyes within ten generations. Mankind has not changed significantly as a genetic, Darwinian entity in 200,000 years. Yet we have changed immensely in the mere flash of time of the last 50,000 years, since Neanderthal, by the accretion of ideas!

“Our civilization has been powerfully affected by the discovery that Nature is strictly governed by impersonal laws.” Truth is discovered, not derived, nor merely agreed upon. In the Prajnaparamita, truth “turns up.” The novelist, Bill Agee said, “Fiction is fact elevated to truth.” Yes, there are Laws (invariant patterns) in epistemology too. Laws are ontology, but there is also an ontology of epistemology!

The whole domain of epistemology lies beyond Homo sapiens, and any species, and any culture, and beyond mass, and energy, and space, and time, and synapses. It is not observer- dependent.

By contrast, ontology and cosmology are intrinsically and unavoidably observer-dependent.

WAYS TO EVALUATE ONTOLOGIES

Definition – explanation – a description that satisfies.

How do we explain things? Here are some of the criteria to distinguish between alternative explanations.